Antennas are influenced by the effect of the ground and by the type
of conductors from which they are constructed. The feedpoint impedance
is the summation of the radiator's self impedance, the mutual impedance
of its image in the ground, and the loss resistance.

The loss resistance is the summation of the R.F. resistance in the conductor,
and the resistance introduced by consumption of power in ground losses
and other media close to the antenna. The conductor's resistance is modified
by the skin-effect which causes the current to only flow in the outer parts,
or skin, of the conductor. The effect causes the resulting resistance to
increases in proportion to the square root of the frequency (see Table
1 and Table 2).

Horizontal antennas are subjected to the influence of a broadsize image
in the ground. The antenna and its image are in anti-phase, so radiation
tends to be cancelled at low angles and the radiation resistance is lowered
because the mutual impedance of the image is subtracted from the self-impedance
of the driven element.

Modelling

To quantify the effects of locating antennas above real ground, I have
once again resorted to computer modelling using NEC-2 (Ref 1). All simulation
results have been performed with 1.22mm diameter wire (SWG #18) and assume
lossless conductors.

The simulation results are displayed graphically so you can determine
the trends and evaluate your own antennas. The soil parameters for each
simulation are enclosed in square brackets. For example, [13,5] represents
ground with a relative dielectric constant of 13 and conductivity of 5
milli-Siemens / m (2S = 1/2ohm, while 4S = 1/4 ohm). The selected values
are: [5,1] for poor soil, [13,5] for average clay soil, [20,30.3] for good
soil and [80,5000] for sea water, which is very close to perfect.

Table 1 and Table 2 are included so you can evaluate conductor resistance
losses due to the skin effect (Ref 2).

Results

Figure 1 shows the effects of various types of grounds on a 1.825 MHz
horizontal 0.5 wave dipole between 0.01 and 0.25 wavelengths above the
ground. Note how over poorer soils the feedpoint impedance is dramatically
higher than the resistance for perfect ground. Notice how the feedpoint
resistance for a horizontal antenna becomes very low as the antenna approaches
a perfect earth. (The feedpoint resistance of a perfect conductor over
a perfectly conducting ground is the radiation resistance of the antenna.)

Figure 2 illustrates the overall antenna efficiency; a measure of how
much power is radiated over the hemisphere, compared to power fed into
the antenna (the missing power is absorbed by the ground).

Figure 3 illustrates the effect upon the maximum gain. (However, at
160m, poor ground means the maximum gain is at an elevation of 90 degrees
- ie straight up!)

Figures 4, 5, and 6 show the effect upon feedpoint resistance at 3.5
MHz, 7.0 MHz and 14.0 MHz respectively.

Table 1 and Table 2 give the R.F. resistance of round copper wire at
various frequencies. The values are listed in ohms per wavelength. You
must halve these values for wires carrying cosinusoidal currents. The resulting
value when added to the graphical results accounts for losses in a non-ideal
conductor.

Conclusions

The radiation resistance of a horizontal antenna is lowered as the antenna
is brought closer to the ground because self and mutual impedances subtract.

As a horizontal antenna approaches lossy media the feedpoint resistance
rises due to increasing power losses in the media. You must be wary of
this tendency for low antennas to apparently present a good feedpoint resistance.

Poor conductors, or inappropriate conductor sizes, will also introduce
loss resistance. This effect is particularly noticeable in cases such as
loading coils.

By comparison though, a horizontal radiator has less ground loss than
a vertical antenna mounted at the same average height (compare the graphs
for horizontals against those for verticals from Ref 3.0).

This article was first published in Amateur
Radio Volume 64 No 10, October 1996 which is the journal of the Wireless
Institute of Australia. Both the author and the WIA hold copyright. No
reproduction is permitted for commercial purposes without express permission
of the copyright holders.